Question: Margo wants to build a rectangular fence around her garden, and she has $24$ meters of wood. Which of these dimensions will give Margo the largest area? Choose 1 answer: Choose 1 answer: (Choice A) A $6$ meters by $6$ meters (Choice B) B $8$ meters by $4$ meters (Choice C) C $10$ meters by $2$ meters
Solution: Let's find the area of each rectangle to see which one has the largest area. $\text{Area of a rectangle} = \text{width} \times \text{height}$ $8$ meters by $4$ meters $8\text{ m}$ $8\text{ m}$ $$ $4\text{ m}$ $4\text{ m}$ $\text{Area}=8\text{ m}\times4\text{ m} = 32\text{ square meters}$ $10$ meters by $2$ meters $10\text{ m}$ $10\text{ m}$ $$ $2\text{ m}$ $2\text{ m}$ $\text{Area}={10}\text{ m}\times2\text{ m} = 20\text{ square meters}$ $6$ meters by $6$ meters $6\text{ m}$ $6\text{ m}$ $$ $6\text{ m}$ $6\text{ m}$ $\text{Area}={6}\text{ m}\times6\text{ m} = 36\text{ square meters}$ $36\text{ m}^2 > 32\text{ m}^2> 20\text{ m}^2$ The garden with the dimensions of $6\text{ meters}$ by $6\text{ meters}$ has the largest area.